12.5.30 problem 27

Internal problem ID [1654]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 27
Date solved : Monday, January 27, 2025 at 05:18:05 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }&=3 x^{2}+4 y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=\sqrt {3} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 15

dsolve([x*y(x)*diff(y(x),x)=3*x^2+4*y(x)^2,y(1) = 3^(1/2)],y(x), singsol=all)
 

\[ y = \sqrt {4 x^{6}-1}\, x \]

✓ Solution by Mathematica

Time used: 0.713 (sec). Leaf size: 18

DSolve[{x*y[x]*D[y[x],x]==3*x^2+4*y[x]^2,y[1]==Sqrt[3]},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \sqrt {4 x^6-1} \]